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Title: An analytic representation of weak mutually unbiased bases
Author: Olupitan, Tominiyi E.
ISNI:       0000 0004 7231 5730
Awarding Body: University of Bradford
Current Institution: University of Bradford
Date of Award: 2016
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Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Finite quantum systems ; Weak mutually unbiased bases ; Finite geometry ; Theta functions